Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics

TL;DR

This paper reviews non-inertial frames in Minkowski space-time, introduces a family of such frames via point-dependent Lorentz transformations, and discusses replacing mathematical observers with dynamical ones and their implications for relativistic quantum mechanics.

Contribution

It provides explicit expressions for non-inertial frames derived from inertial ones and explores replacing mathematical observers with dynamical particles in non-inertial relativistic quantum mechanics.

Findings

Explicit non-inertial frame expressions from Lorentz transformations

Proposal for dynamical observers replacing mathematical ones

Comments on Unruh-DeWitt detectors and quantum mechanics transition

Abstract

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how to define Unruh-DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.